Computational Atomic Physics

1. Electron-Atom Scattering Theory: An Overview.- Abstract.- 1.1 Introduction.- 1.2 Potential Scattering.- 1.3 Perturbation Approaches.- 1.4 The Close-Coupling Expansion.- 1.5 Computer Program for Potential Scattering.- 1.5.1 Description of the Input Data.- 1.5.2 Test-Run Data.- 1.6 Summary.- 1.7 Suggested Problems.- Acknowledgments.- References.- 2. Core Potentials for Quasi One-Electron Systems.- Abstract.- 2.1 Introduction.- 2.2 Theory.- 2.3 The Algorithm.- 2.4 Computer Program.- 2.4.1 Program Structure.- 2.4.2 Description of the Input Parameters.- 2.5 Test Run.- 2.6 Summary.- 2.7 Suggested Problems.- Acknowledgments.- References.- 3. Energies and Oscillator Strengths Using Configuration Interaction Wave Functions.- Abstract.- 3.1 Introduction.- 3.2 Hydrogen-Like Ions.- 3.2.1 Angular Momentum.- 3.2.2 Commuting Operators.- 3.2.3 Fine Structure.- 3.3 Two-Electron Atoms and Ions.- 3.3.1 Wave Functions for Two-Electron Ions.- 3.3.2 Variational Principle.- 3.3.3 Application to the Two-Electron Ground-State Energy.- 3.4 Many-Electron Atoms and Ions.- 3.4.1 Hartree’s Method.- 3.4.2 The Hartree-Fock Method.- 3.5 Configuration Interaction Methods.- 3.5.1 Optimization of the Expansion Coefficients.- 3.5.2 Optimization of the CSF.- 3.5.3 Correlation Energy.- 3.5.4 Choice of Configurations.- 3.5.5 Calculation of Several States Simultaneously.- 3.6 Transition Probabilities and Oscillator Strengths.- 3.6.1 Dipole Approximation.- 3.6.2 Length and Velocity Forms.- 3.6.3 The Effect of Electron Correlation.- 3.6.4 Selection Rules.- 3.7 The Codes.- 3.7.1 Running of the Codes.- 3.7.2 Sample Radial Data.- 3.8 Examples.- 3.9 Summary.- 3.10 Suggested Problems.- 3.10.1 He-Like Ions.- 3.10.2 Be-Like Ions.- 3.10.3 Ground State of Carbon.- References.- 4. The Distorted-Wave Method for Elastic Scattering and Atomic Excitation.- Abstract.- 4.1 Introduction.- 4.2 Theory.- 4.2.1 Distorted-Wave Series.- 4.2.2 Discussion of Distorting Potentials Ui and Uf.- 4.3 First-Order Amplitudes.- 4.3.1 Inelastic Scattering.- 4.3.2 Elastic Scattering.- 4.4 Partial-Wave Expansion of the T Matrix.- 4.4.1 Inelastic Scattering.- 4.4.2 Elastic Scattering.- 4.4.3 Differential Cross Sections.- 4.5 Computer Program.- 4.5.1 Radial Mesh.- 4.5.2 Numerical Technique.- 4.5.3 Program Input.- 4.5.4 Sample Input and Output.- 4.6 Summary.- 4.7 Suggested Problems.- Acknowledgments.- References.- 5. Distorted-Wave Methods for Ionization.- Abstract.- 5.1 Introduction.- 5.2 Theory.- 5.3 Reduction of the (e,2e) Amplitudes to Computational Form.- 5.3.1 Distorted-Wave Born Approximation: Direct Amplitude.- 5.3.2 Radial Partial Waves.- 5.3.3 Exchange Amplitude.- 5.3.4 Radial Integration.- 5.3.5 Distorted-Wave Impulse Approximation.- 5.4 Computer Program.- 5.4.1 Input.- 5.4.2 Calculation of the Differential Cross Section.- 5.4.3 Sample Input.- 5.4.4 Sample Output.- 5.5 Summary.- 5.6 Suggested Problems.- Acknowledgments.- References.- 6. The Close-Coupling Approximation.- Abstract.- 6.1 Introduction.- 6.2 Theory.- 6.2.1 The Close-Coupling Equations.- 6.2.2 Boundary Conditions and Cross Sections.- 6.3 The Numerical Solution of the Close-Coupling Equations.- 6.3.1 The Power-Series Expansion About the Origin.- 6.3.2 Asymptotic Correction Procedures.- 6.4 The Born Approximation.- 6.5 Computer Program.- 6.5.1 The Radial Meshes.- 6.5.2 Numerical Procedures.- 6.5.3 Convergence Criteria.- 6.5.4 Program Input.- 6.5.5 Sample Input and Output.- 6.6 Summary.- 6.7 Suggested Problems.- Acknowledgments.- References.- 7. The R-Matrix Method.- Abstract.- 7.1 Introduction.- 7.2 General R-Matrix Theory.- 7.3 Electron-Hydrogen-like Ion Scattering.- 7.4 Computational Solution of the Electron-Hydrogen-Like Ion-Collision Problem.- 7.4.1 The Inner Region.- 7.4.2 Outer Region Problem.- 7.5 Computer Program.- 7.5.1 Description of Input Data for the Program Package PACK1.- 7.5.2 Description of Input Data for PACK2.- 7.5.3 Sample Input and Output.- 7.5.4 Notes on Running the Codes.- 7.6 Summary.- 7.7 Suggested Problems.- Acknowledgments.- References.- 8. Momentum-Space Convergent-Close-Coupling Method for a Model e-H Scattering Problem.- Abstract.- 8.1 Introduction.- 8.2 Theory.- 8.2.1 Close-Coupling Equations.- 8.2.2 Target-State Manifold.- 8.2.3 Ensuring the Uniqueness of Solution.- 8.2.4 Momentum-Space Convergent-Close-Coupling.- 8.2.5 Cross Sections.- 8.3 Numerical Solution.- 8.3.1 Diagonalizing the Target Hamiltonian.- 8.3.2 Calculating V Matrix Elements.- 8.3.3 Solution of the Coupled Equations.- 8.4 Computer Program.- 8.4.1 Input.- 8.4.2 Output.- 8.4.3 Typical Usage.- 8.5 Summary.- 8.6 Suggested Problems.- References.- 9. The Calculation of Spherical Bessel and Coulomb Functions.- Abstract.- 9.1 Introduction.- 9.2 Spherical Bessel Functions.- 9.3 Recurrence Relations for Spherical Bessel Functions.- 9.4 Evaluation of the Continued Fraction.- 9.5 The Programs SBESJY and RICBES.- 9.6 Recurrence Relations for Coulomb Functions.- 9.7 The Program C0UL90.- 9.8 Test Data.- 9.8.1 Sample Input Data.- 9.8.2 Sample Output Data.- 9.9 Summary.- 9.10 Suggested Problems.- Acknowledgments.- References.- 10. Scattering Amplitudes for Electron-Atom Scattering.- Abstract.- 10.1 Introduction.- 10.2 Definition of the Scattering Amplitudes.- 10.3 Convergence of Partial Wave Expansions.- 10.3.1 Effective Range Theory for Elastic Scattering.- 10.3.2 Unitarized Born Approximation for Excitation.- 10.3.3 Exponential Fitting.- 10.4 Symmetry Properties of Scattering Amplitudes.- 10.5 Computer Program.- 10.5.1 Description of the Input Data.- 10.5.2 Test Runs.- 10.6 Summary.- 10.7 Suggested Problems.- Acknowledgments.- References.- 11. Density Matrices: Connection Between Theory and Experiment.- Abstract.- 11.1 Introduction.- 11.2 Scattering Amplitudes.- 11.3 Density Matrices.- 11.4 Irreducible Tensor Operators and State Multipoles.- 11.4.1 Basic Definitions.- 11.4.2 Coupled Systems.- 11.4.3 Time Evolution of State Multipoles: Quantum Beats.- 11.4.4 Time Integration over Quantum Beats.- 11.5 Observables.- 11.5.1 Generalized ST U Parameters.- 11.5.2 Generalized Stokes Parameters.- 11.6 2S ? 2P° Transitions.- 11.6.1 General Description of an Excited 2P° State.- 11.6.2 Relationship to Experimental Observables.- 11.7 Computer Program.- 11.7.1 Description of the Input Data.- 11.7.2 Test Run.- 11.8 Summary.- 11.9 Suggested Problems.- Acknowledgments.- References.